A graha is not read in isolation but through the several tables that make up a Panchanga and a chart. It rules no weekday, because the seven-day week is built from the seven visible grahas and the two nodes stand outside that set. It holds 18 years of the Vimshottari dasha cycle, and it is lord of three of the twenty-seven nakshatras, Ardra, Swati and Shatabhisha, spaced nine apart so that the nine grahas cover the twenty-seven exactly three times over.
The Vimshottari dasha system divides a notional lifetime of 120 years among the nine grahas in a fixed order, Ketu, Venus, Sun, Moon, Mars, Rahu, Jupiter, Saturn and Mercury, with fixed lengths that sum to exactly 120. Which period a person begins life in is determined by the nakshatra the Moon occupied at birth, and how far through that period, by how far through the nakshatra the Moon had travelled.
In the scheme of dignities it is assigned an exaltation on which the classical sources do not agree, and dignity is what the classical rules for strength are built on, since a graha in its own sign or its exaltation is read as able to act and one in its fall as constrained.
Rahu is not a body. It is the ascending node of the Moon's orbit, the point where the Moon crosses the plane of the ecliptic going north, and it is one of the two points at which eclipses can occur. That is why the tradition calls the nodes the shadow grahas and tells the story of a severed demon who swallows the Sun and Moon: the mythology and the eclipse geometry are describing the same thing.